A Varying-Coefficient Approach To Estimation And Extrapolation Of Household Size

Household formation analysis is both a multidimensional economical and statistical problem of great complexity. Since most of the literature tries to incorporate multiple economic aspects, there is, considering the extraordinary practical relevance of the problem, a remarkable gap between theory and application in this field. This paper tries to diminish this gap by a comprehensive treatise on the statistical site of the problem. Thus, we develop a model of household composition, where the evolution of the household membership rates is captured by a logit link-function and a multinomial distribution, which automatically fulfills the non-negativity and adding-up restrictions of the underlying probabilities. We use a varying-coefficients procedure by polynomially smoothing the household membership rates over age for every household size class and assuming a linear predictor in other variables. As an application we estimated and extrapolated the distribution of household sizes of an autonomous region using population register data. Our sample consisted of approximately 450,000 people living in about 170,000 households, grouped into nine different household size classes and classified into age classes from 0 to 90. The data covers a time span of 12 years, from 1986 to 1997. Empirical results show the robustness of the procedure even in case of low cell frequencies. Thus, there is no need for regional or age-group aggregations.